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In recent years, abundant DNA sequence data has led to widespread interest in computational methods for detecting sequences that are evolving faster, slower, or by different patterns of evolution than would be expected under neutral drift, and hence are likely to have evolutionarily important biological functions. These methods are providing new insights into the evolutionary dynamics that have shaped present-day genomes, and they are beginning to reveal the genetic basis of key differences between species, including some of the specific differences that differentiate humans from other mammals. In this talk, I will review established methods for detecting positive and lineage-specific selection, focusing on likelihood ratio tests based on continuous-time Markov models of nucleotide and codon substitution. In addition, I will discuss new methods for detecting lineage-specific selection, and for evaluating the statistical significance of apparent lineage-specific changes in evolutionary rate. I will also discuss a comprehensive study of positively selected protein-coding genes in mammals that my group has recently completed. The talk will be geared for an audience of computational and statistical scientists, and no background in biology is required.